I think you have a digitizer that is failing, but before giving up on the phone try this: Factory Data Reset - With your Motorola Droid still powered "Off," slide open the keyboard.
Press and hold the "X" button on the keyboard while pressing the "Power/Unlock" button, located next to the 3.5mm headphone jack. Continue holding down the buttons until a yellow triangle "Warning Sign" appears on the screen.
Once the yellow warning sign appears, press the physical "Volume UP" and "Camera" buttons simultaneously until a new menu appears. This may take several attempts before success.
From the new menu that appears on-screen, go down to the "wipe data/factory reset" option using the Directional-Pad next to the keyboard, and press the "Center" button on the D-Pad to confirm.
Scroll down to the "Yes -- delete all user data" and press the "Center" button on the D-Pad once more. That's it! When your Motorola Droid is done wiping all saved applications, information, and settings, your device will be back to the factory settings.

These have gotten pretty painless lately by following these simple steps: 1. Make sure Backup and Restore are checked in the Privacy setting. 2. When going through the setup after the reset, turn on wifi as soon as you can (assuming it is available). 3. After you have entered your Gmail account info, you will be presented with a screen that has two check boxes. Basically they are "Do you want Google to backup and restore this phone”. Make sure you check both of those. 4. Open the Market app and accept the market terms. 5. Your apps will then automatically reinstall (paid and free). Set the phone aside for a minute or two and let the apps download and install. 6. If rooted, use an app such as titanium backup to restore data only to select apps such as Tapatalk and you will not have to re-enter all your login information. I do this for 3-4 apps (Tapatalk, SPB Shell, etc.).

I've been flashing new roms/updates about once per day lately and I can be up and running with all my apps and settings back in place in less than 20 minutes. It's pretty painless now.

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